A cover with an opening structure includes an enclosure defining an opening, a cover rotatably mounted to the enclosure, and a driver mounted in the enclosure. The cover is engaged with the enclosure to cover the opening. The enclosure includes a holder defining a first slot. The first slot includes a first position and a second position. The cover includes a connecting arm, a camshaft and a pivot protruding from opposite sides of the connecting arm, and the pivot is slidably located in the first slot. When the cover is covering the opening, the pivot is located at the first position, and the diver resists the camshaft elastically. When the cover is disengaged from the enclosure, the pivot is driven by release of elasticity to slide from the first position to the second position to rotate the cover to open.